P7A77: I think I have it...
plays on the point of symmetry. or a, taking away a liberty, is the best response I can find - the sequence from can be played on whichever side white does not respond. Playing at first allows black to avoid pushing out on both sides, which loses liberties.
Alex: This is what I was going to say, and I think it's correct. Few people would find this sort of tesuji in an actual game, but it's kind of obvious as a problem, since you know that a) it wouldn't be much of a problem if simply pushing out would work, b) it's a problem, so there must be a solution, and c) there really isn't anything else to consider.
Unless someone can refute this, I think it can be moved to the solutions page.